Diff-in-Diff, population weights and parallel trends: part 1

I’m going to be trying to re-enter writing about econometrics. I have a few papers I need to work through closely, and it’s just a good time to keep retooling more generally. I also want to give my subscribing readers more value for being a subscriber, and therefore am just going to go back to my randomized paywalls. And today, I had Cosmos once again flip a coin three times to see if I would be paywalling and indeed, today is a randomized paywall day!

But before I do, I wanted to tell you a little about what this post is about. This post is going to be part 1 in a couple of posts that shows the exact conditions under which you can identify using diff-in-diff both an unweighted causal effect and a population weighted causal effect. I’m going to show you this formally using something I’ve been working on. And then I’m going to show you in a subsequent post code and output from a simulation that illustrates it. But the punch line is this:

just because parallel trends holds with aggregate data does not mean it will hold with population weighted data. The conditions under which both hold and not hold is what this series is about.

So with that, let’s go! Thank you again for all your support! Please consider becoming a paying subscriber. Supply curves slope upwards and after a long hiatus of paywalling, I’m going to be going back to doing so and writing about econometrics, and new papers I’m investing time in, particularly as I prepare for my new courses next spring at Harvard (including a PhD course).